{"cells":[{"cell_type":"markdown","metadata":{"id":"4jQLbOS7JhxD"},"source":["# PyTorch Introduction\n","\n","Today, we will be intoducing PyTorch, \"an open source deep learning platform that provides a seamless path from research prototyping to production deployment\".\n","\n","This notebook is by no means comprehensive. If you have any questions the documentation and Google are your friends.\n","\n","Goal takeaways:\n","- Automatic differentiation is a powerful tool\n","- PyTorch implements common functions used in deep learning"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Rw-LPR3HJhxJ"},"outputs":[],"source":["import torch\n","import torch.nn as nn\n","import torch.nn.functional as F\n","\n","import matplotlib.pyplot as plt\n","from mpl_toolkits.mplot3d import Axes3D\n","\n","import numpy as np\n","\n","torch.manual_seed(446)\n","np.random.seed(446)"]},{"cell_type":"markdown","metadata":{"id":"GQDY0uBiJhxJ"},"source":["## Tensors and relation to numpy\n","\n","By this point, we have worked with numpy quite a bit. PyTorch's basic building block, the `tensor` is similar to numpy's `ndarray`"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"LHKLjTFWJhxK","outputId":"aa87f24d-68e6-4213-d1c6-81157a904eb5","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804923204,"user_tz":420,"elapsed":233,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["x_numpy, x_torch\n","Numpy: [0.1 0.2 0.3]\n","Torch: tensor([0.1000, 0.2000, 0.3000])\n","\n","to and from numpy and pytorch\n","Numpy -> Torch: tensor([0.1000, 0.2000, 0.3000], dtype=torch.float64)\n","Torch -> Numpy: [0.1 0.2 0.3]\n","\n","x+y\n","Numpy: [3.1 4.2 5.3]\n","Torch: tensor([3.1000, 4.2000, 5.3000])\n","\n","norm\n","Numpy: 0.374166\n","Torch: 0.374166\n","\n","mean along the 0th dimension\n","Numpy: [2. 3.]\n","Torch: tensor([2., 3.])\n"]}],"source":["# we create tensors in a similar way to numpy nd arrays\n","x_numpy = np.array([0.1, 0.2, 0.3])\n","x_torch = torch.tensor([0.1, 0.2, 0.3])\n","print('x_numpy, x_torch')\n","print(f\"Numpy: {x_numpy}\")\n","print(f\"Torch: {x_torch}\")\n","print()\n","\n","# to and from numpy, pytorch\n","print('to and from numpy and pytorch')\n","print(f\"Numpy -> Torch: {torch.from_numpy(x_numpy)}\")\n","print(f\"Torch -> Numpy: {x_torch.numpy()}\")\n","print()\n","\n","# we can do basic operations like +-*/\n","y_numpy = np.array([3,4,5.])\n","y_torch = torch.tensor([3,4,5.])\n","print(\"x+y\")\n","print(f\"Numpy: {x_numpy + y_numpy}\")\n","print(f\"Torch: {x_torch + y_torch}\")\n","print()\n","\n","# many functions that are in numpy are also in pytorch\n","print(\"norm\")\n","print(f\"Numpy: {np.linalg.norm(x_numpy):.6g}\")\n","print(f\"Torch: {torch.norm(x_torch):.6g}\")\n","print()\n","\n","# to apply an operation along a dimension,\n","# we use the dim keyword argument instead of axis\n","x_numpy = np.array([[1,2],[3,4.]])\n","x_torch = torch.tensor([[1,2],[3,4.]])\n","print(\"mean along the 0th dimension\")\n","print(f\"Numpy: {np.mean(x_numpy, axis=0)}\")\n","print(f\"Torch: {torch.mean(x_torch, dim=0)}\")\n"]},{"cell_type":"markdown","metadata":{"id":"YgGuAT7-JhxK"},"source":["### `Tensor.view`\n","We can use the `Tensor.view()` function to reshape tensors similarly to `numpy.reshape()`.\n","\n","**Note:** A imporant difference between `view` and `reshape` is that `view` returns reference to the same tensor as the one passed in. This means that if we modify values in the output of `view` they will also change for its input. This can lead to some issues. For more information see [PyTorch](https://pytorch.org/docs/stable/tensor_view.html).\n","\n","Similarly to `reshape` it can also automatically calculate the correct dimension if a `-1` is passed in. This is useful if we are working with batches, but the batch size is unknown."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"c87j1vX4JhxL","outputId":"1414a3a8-09ee-4531-c3e9-41835a9eb0c8","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804926243,"user_tz":420,"elapsed":582,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["torch.Size([10000, 3, 28, 28])\n","torch.Size([10000, 3, 784])\n","torch.Size([10000, 3, 784])\n","torch.Size([10000, 3, 784])\n"]}],"source":["# \"MNIST\" - like\n","N, C, W, H = 10000, 3, 28, 28\n","X = torch.randn((N, C, W, H))\n","\n","print(X.shape)\n","print(X.view(N, C, 784).shape)\n","print(X.view(-1, C, 784).shape) # automatically choose the 0th dimension\n","\n","# Alternatively you can use torch.reshape, though it's less commonly used\n","print(torch.reshape(X, (-1, C, 784)).shape)"]},{"cell_type":"markdown","metadata":{"id":"xYZQu4eyJhxM"},"source":["## PyTorch as an auto grad framework\n","\n","Main benefit of PyTorch is that it keeps track of gradients for us, as we do the calculations.\n","This is done through computation graphs, which you can read more about in Appendix 1 of this notebook.\n","The example below shows how to use these gradients.\n","\n","Consider the function $f(x) = (x-2)^2$.\n","\n","Q: Compute $\\frac{d}{dx} f(x)$ and then compute $f'(1)$.\n","\n","We make a `backward()` call on the leaf variable (`y`) in the computation, computing all the gradients of `y` at once."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"mpNsPVaFJhxM","outputId":"61b523d1-8db8-4ba1-9ae0-c33fcd1c7eea","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804928168,"user_tz":420,"elapsed":3,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["Analytical f'(x): tensor([-2.], grad_fn=)\n","PyTorch's f'(x): tensor([-2.])\n"]}],"source":["def f(x):\n"," return (x-2)**2\n","\n","def fp(x):\n"," return 2*(x-2)\n","\n","x = torch.tensor([1.0], requires_grad=True)\n","\n","y = f(x)\n","y.backward()\n","\n","print('Analytical f\\'(x):', fp(x))\n","print('PyTorch\\'s f\\'(x):', x.grad)\n"]},{"cell_type":"markdown","metadata":{"id":"w2ui_X5kJhxM"},"source":["It can also find gradients of functions.\n","\n","Let $w = [w_1, w_2]^T$\n","\n","Consider $g(w) = 2w_1w_2 + w_2\\cos(w_1)$\n","\n","Q: Compute $\\nabla_w g(w)$ and verify $\\nabla_w g([\\pi,1]) = [2, \\pi - 1]^T$"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"XCmYCypXJhxN","outputId":"462a2716-a9ed-4417-a851-30a25cd8be90","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698805960655,"user_tz":420,"elapsed":195,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["Analytical grad g(w) tensor([2.0000, 5.2832])\n","PyTorch's grad g(w) tensor([2.0000, 5.2832])\n"]}],"source":["def g(w):\n"," return 2*w[0]*w[1] + w[1]*torch.cos(w[0])\n","\n","def grad_g(w):\n"," return torch.tensor([2*w[1] - w[1]*torch.sin(w[0]), 2*w[0] + torch.cos(w[0])])\n","\n","w = torch.tensor([np.pi, 1], requires_grad=True)\n","\n","z = g(w)\n","z.backward()\n","\n","print('Analytical grad g(w)', grad_g(w))\n","print('PyTorch\\'s grad g(w)', w.grad)"]},{"cell_type":"markdown","metadata":{"id":"palemKNRJhxN"},"source":["## Using the gradients - Linear regression using GD with torch\n","Now that we have gradients, we can use our favorite optimization algorithm: gradient descent!\n","\n","**Note**: This example is an illustration to connect ideas we have seen before to PyTorch's way of doing things. We will see how to do this in the \"PyTorchic\" way in the next example.\n","\n","But first lets generate synthetic data to solve on our problem."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"80oVXI15JhxO","outputId":"50018415-808a-4abc-a823-ff6285e57191","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698805962749,"user_tz":420,"elapsed":177,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["X shape torch.Size([50, 2])\n","y shape torch.Size([50, 1])\n","w shape torch.Size([2, 1])\n"]}],"source":["# make a simple linear dataset with some noise\n","d = 2\n","n = 50\n","\n","X = torch.randn(n,d)\n","true_w = torch.tensor([[-1.0], [2.0]])\n","y = X @ true_w + torch.randn(n,1) * 0.1\n","print('X shape', X.shape)\n","print('y shape', y.shape)\n","print('w shape', true_w.shape)\n"]},{"cell_type":"markdown","metadata":{"id":"fPMrxyGqJhxO"},"source":["We will also define a helper function to visualize result's of what $\\hat{w}$ we have learned."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Jzl5zI8pJhxO"},"outputs":[],"source":["def visualize_fun(w, title, num_pts=20):\n","\n"," x1, x2 = np.meshgrid(np.linspace(-2,2, num_pts), np.linspace(-2,2, num_pts))\n"," X_plane = torch.tensor(np.stack([np.reshape(x1, (num_pts**2)), np.reshape(x2, (num_pts**2))], axis=1)).float()\n"," y_plane = np.reshape((X_plane @ w).detach().numpy(), (num_pts, num_pts))\n","\n"," fig = plt.figure()\n"," plt3d = fig.add_subplot(111, projection='3d')\n"," plt3d.plot_surface(x1, x2, y_plane, alpha=0.2)\n","\n"," plt3d.scatter(X[:,0].numpy(), X[:,1].numpy(), y.numpy(), c='r', marker='o')\n","\n"," plt3d.set_xlabel('$X_1$')\n"," plt3d.set_ylabel('$X_2$')\n"," plt3d.set_zlabel('$Y$')\n","\n"," plt.title(title)\n"," plt.show()"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"_RCypV6yJhxO","outputId":"4855287a-9647-4831-fde1-e27eccf5d733","colab":{"base_uri":"https://localhost:8080/","height":433},"executionInfo":{"status":"ok","timestamp":1698806292762,"user_tz":420,"elapsed":4,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["
"],"image/png":"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\n"},"metadata":{}}],"source":["visualize_fun(true_w, 'Dataset and true $w$')"]},{"cell_type":"markdown","metadata":{"id":"BwfAi7BaJhxP"},"source":["### Algorithm for Linear regression using GD with automatically computed derivatives\n","\n","**Note**: This example is an illustration to connect ideas we have seen before to PyTorch's way of doing things. We will see how to do this in the \"PyTorchic\" way in the next example."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"nTpC3BbeJhxP","outputId":"eb7f99ca-ad29-49a5-bcfe-f99cde564cc8","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698805995803,"user_tz":420,"elapsed":183,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["iter,\tloss,\tw\n","0,\t5.77,\t[0.68696296 0.25955352]\n","1,\t4.24,\t[0.42487893 0.48802835]\n","2,\t3.12,\t[0.20485593 0.68842417]\n","3,\t2.29,\t[0.01968367 0.8636641 ]\n","4,\t1.69,\t[-0.13651094 1.0165186 ]\n","5,\t1.25,\t[-0.2685325 1.149562 ]\n","6,\t0.92,\t[-0.38032806 1.2651515 ]\n","7,\t0.68,\t[-0.47515318 1.3654212 ]\n","8,\t0.50,\t[-0.5557032 1.4522861]\n","9,\t0.37,\t[-0.62421775 1.5274527 ]\n","10,\t0.28,\t[-0.6825636 1.5924329]\n","11,\t0.21,\t[-0.73230195 1.6485596 ]\n","12,\t0.15,\t[-0.7747419 1.697004 ]\n","13,\t0.12,\t[-0.810984 1.7387912]\n","14,\t0.09,\t[-0.8419558 1.7748165]\n","15,\t0.07,\t[-0.8684405 1.8058598]\n","16,\t0.05,\t[-0.89110094 1.8325992 ]\n","17,\t0.04,\t[-0.91049886 1.855623 ]\n","18,\t0.03,\t[-0.92711115 1.8754417 ]\n","19,\t0.02,\t[-0.9413433 1.8924967]\n","\n","true w\t\t [-1. 2.]\n","estimated w\t [-0.9413433 1.8924967]\n"]}],"source":["# define a linear model with no bias\n","def model(X, w):\n"," return X @ w\n","\n","# the residual sum of squares loss function\n","def rss(y, y_hat):\n"," return torch.norm(y - y_hat)**2 / n\n","\n","# Define hyperparameters\n","step_size = 0.1\n","\n","# And starting w\n","w = torch.tensor([[1.], [0]], requires_grad=True)\n","\n","print('iter,\\tloss,\\tw')\n","for i in range(20):\n"," y_hat = model(X, w)\n"," loss = rss(y, y_hat)\n","\n"," loss.backward() # compute the gradient of the loss\n","\n"," w.data = w.data - step_size * w.grad # do a gradient descent step\n","\n"," print('{},\\t{:.2f},\\t{}'.format(i, loss.item(), w.view(2).detach().numpy()))\n","\n"," # We need to zero the grad variable since the backward()\n"," # call accumulates the gradients in .grad instead of overwriting.\n"," # The detach_() is for efficiency. You do not need to worry too much about it.\n"," w.grad.detach()\n"," w.grad.zero_()\n","\n","print('\\ntrue w\\t\\t', true_w.view(2).numpy())\n","print('estimated w\\t', w.view(2).detach().numpy())"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"JIDXZqI1JhxP","outputId":"608292b1-f04c-438c-cc50-bdeee1754695","colab":{"base_uri":"https://localhost:8080/","height":435},"executionInfo":{"status":"ok","timestamp":1698806422755,"user_tz":420,"elapsed":597,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["
"],"image/png":"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\n"},"metadata":{}}],"source":["visualize_fun(w, 'Dataset with learned $w$ (Manual GD)')"]},{"cell_type":"markdown","metadata":{"id":"5U9Xi9AmJhxP"},"source":["## torch.nn.Module\n","\n","`Module` is PyTorch's way of performing operations on tensors. Modules are implemented as subclasses of the `torch.nn.Module` class. All modules are callable and can be composed together to create complex functions.\n","\n","[`torch.nn` docs](https://pytorch.org/docs/stable/nn.html)\n","\n","Note: most of the functionality implemented for modules can be accessed in a functional form via `torch.nn.functional`, but these require you to create and manage the weight tensors yourself. **Note:** This\n","\n","[`torch.nn.functional` docs](https://pytorch.org/docs/stable/nn.html#torch-nn-functional).\n","\n","### Linear Module\n","The bread and butter of modules is the Linear module which does a linear transformation with a bias. It takes the input and output dimensions as parameters, and creates the weights in the object. It is just a matrix multiplication and addition of bias:\n","\n","$$ f(X) = XW + b, f: \\mathbb{R}^{n \\times d} \\rightarrow \\mathbb{R}^{n \\times h} $$\n","\n","where $X \\in \\mathbb{R}^{n \\times d}$, $W \\in \\mathbb{R}^{d \\times h}$ and $b \\in \\mathbb{R}^{h}$\n","\n","Unlike how we initialized our $w$ manually, the Linear module automatically initializes the weights randomly. For minimizing non convex loss functions (e.g. training neural networks), initialization is important and can affect results. If training isn't working as well as expected, one thing to try is manually initializing the weights to something different from the default. PyTorch implements some common initializations in `torch.nn.init`.\n","\n","[`torch.nn.init` docs](https://pytorch.org/docs/stable/nn.html#torch-nn-init)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"Tur-YOxpJhxQ","outputId":"dbb7de87-63bb-4773-ca6d-891fc38d77e8","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804986527,"user_tz":420,"elapsed":135,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["example_tensor torch.Size([2, 3])\n","transformed torch.Size([2, 4])\n","\n","We can see that the weights exist in the background\n","\n","W: Parameter containing:\n","tensor([[ 0.2151, -0.2631, 0.4498],\n"," [-0.3092, 0.3098, -0.4239],\n"," [-0.0499, -0.2222, 0.0085],\n"," [-0.0356, 0.5260, 0.4925]], requires_grad=True)\n","b: Parameter containing:\n","tensor([-0.0887, 0.3944, 0.4080, 0.2182], requires_grad=True)\n"]}],"source":["d_in = 3\n","d_out = 4\n","linear_module = nn.Linear(d_in, d_out)\n","\n","example_tensor = torch.tensor([[1.,2,3], [4,5,6]])\n","# applys a linear transformation to the data\n","transformed = linear_module(example_tensor)\n","print('example_tensor', example_tensor.shape)\n","print('transformed', transformed.shape)\n","print()\n","print('We can see that the weights exist in the background\\n')\n","print('W:', linear_module.weight)\n","print('b:', linear_module.bias)"]},{"cell_type":"markdown","metadata":{"id":"9lDZ2EtyJhxQ"},"source":["### Activation functions\n","PyTorch implements a number of activation functions including but not limited to `ReLU`, `Tanh`, and `Sigmoid`. Since they are modules, they need to be instantiated."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"a5vAZ1lwJhxQ","outputId":"74979fff-17d5-4d14-8fdb-e56367aa32e1","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804988350,"user_tz":420,"elapsed":2,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["example_tensor tensor([-1., 1., 0.])\n","activated tensor([0., 1., 0.])\n"]}],"source":["activation_fn = nn.ReLU() # we instantiate an instance of the ReLU module\n","example_tensor = torch.tensor([-1.0, 1.0, 0.0])\n","activated = activation_fn(example_tensor)\n","print('example_tensor', example_tensor)\n","print('activated', activated)"]},{"cell_type":"markdown","metadata":{"id":"zXH-1ipXJhxQ"},"source":["### Sequential\n","\n","Many times, we want to compose Modules together. `torch.nn.Sequential` provides a good interface for composing simple modules."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"8ztmvadTJhxQ","outputId":"dc2a9d36-f206-41b4-ad75-2a60bc48c490","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804989915,"user_tz":420,"elapsed":155,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["transformed torch.Size([2, 1])\n"]}],"source":["d_in = 3\n","d_hidden = 4\n","d_out = 1\n","model = torch.nn.Sequential(\n"," nn.Linear(d_in, d_hidden),\n"," nn.Tanh(),\n"," nn.Linear(d_hidden, d_out),\n"," nn.Sigmoid()\n",")\n","\n","example_tensor = torch.tensor([[1.,2,3],[4,5,6]])\n","transformed = model(example_tensor)\n","print('transformed', transformed.shape)"]},{"cell_type":"markdown","metadata":{"id":"MiNTXI1WJhxR"},"source":["Note: we can access *all* of the parameters (of any `nn.Module`) with the `parameters()` method."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"ZL7HKvaYJhxR","outputId":"3878e92e-1d45-4e3c-da0a-a2df38c36558","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804992386,"user_tz":420,"elapsed":155,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["Parameter containing:\n","tensor([[-0.1409, 0.0518, 0.3034],\n"," [ 0.0913, 0.2452, -0.2616],\n"," [ 0.5021, 0.0118, 0.1383],\n"," [ 0.4757, -0.3128, 0.2707]], requires_grad=True)\n","Parameter containing:\n","tensor([-0.3952, 0.1285, 0.1777, -0.4675], requires_grad=True)\n","Parameter containing:\n","tensor([[ 0.0391, -0.4876, -0.1731, 0.4704]], requires_grad=True)\n","Parameter containing:\n","tensor([0.0454], requires_grad=True)\n"]}],"source":["params = model.parameters()\n","\n","for param in params:\n"," print(param)"]},{"cell_type":"markdown","metadata":{"id":"8VgP1_kBJhxR"},"source":["### Loss functions\n","PyTorch implements many common loss functions including `MSELoss` and `CrossEntropyLoss`."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"19cgWAGmJhxR","outputId":"bc8173df-8b59-470c-89a2-a33bc329c5a4","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804995082,"user_tz":420,"elapsed":261,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["tensor(0.6667)\n"]}],"source":["mse_loss_fn = nn.MSELoss()\n","\n","input = torch.tensor([[0., 0, 0]])\n","target = torch.tensor([[1., 0, -1]])\n","\n","loss = mse_loss_fn(input, target)\n","\n","print(loss)"]},{"cell_type":"markdown","metadata":{"id":"CK7MRcgoJhxS"},"source":["## torch.optim\n","PyTorch implements a number of gradient-based optimization methods in `torch.optim`, including Gradient Descent. At the minimum, it takes in the model parameters and a learning rate.\n","\n","Optimizers do not compute the gradients for you, so you must call `backward()` yourself. You also must call the `optim.zero_grad()` function before calling `backward()` since by default PyTorch does and inplace add to the `.grad` member variable rather than overwriting it.\n","\n","This does both the `detach_()` and `zero_()` calls on all tensor's `grad` variables.\n","\n","[`torch.optim` docs](https://pytorch.org/docs/stable/optim.html)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"qtSZzh9lJhxS","outputId":"150b92ab-6d97-499d-f617-4a027c827295","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804996943,"user_tz":420,"elapsed":605,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["model params before: Parameter containing:\n","tensor([[0.1950]], requires_grad=True)\n","model params after: Parameter containing:\n","tensor([[0.2219]], requires_grad=True)\n"]}],"source":["# create a simple model\n","model = nn.Linear(1, 1)\n","\n","# create a simple dataset\n","X_simple = torch.tensor([[1.]])\n","y_simple = torch.tensor([[2.]])\n","\n","# create our optimizer\n","optim = torch.optim.SGD(model.parameters(), lr=1e-2)\n","mse_loss_fn = nn.MSELoss()\n","\n","y_hat = model(X_simple)\n","print('model params before:', model.weight)\n","loss = mse_loss_fn(y_hat, y_simple)\n","optim.zero_grad()\n","loss.backward()\n","optim.step()\n","print('model params after:', model.weight)\n"]},{"cell_type":"markdown","metadata":{"id":"NAOiXlvXJhxS"},"source":["As we can see, the parameter was updated in the correct direction"]},{"cell_type":"markdown","metadata":{"id":"kW-pr275JhxS"},"source":["## Linear regression using GD with torch.nn module\n","\n","Now let's combine what we've learned to solve linear regression in a \"PyTorchic\" way."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"_iVdcw_VJhxS","outputId":"bd4cc092-7c16-4bc5-d013-b0a51993dbcb","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698804998319,"user_tz":420,"elapsed":2,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["iter,\tloss,\tw\n","0,\t4.37,\t[-0.5072827 0.7721884]\n","1,\t2.34,\t[-0.6624694 1.0903175]\n","2,\t1.25,\t[-0.77252483 1.3242052 ]\n","3,\t0.67,\t[-0.85030663 1.4962891 ]\n","4,\t0.36,\t[-0.90505993 1.6230037 ]\n","5,\t0.20,\t[-0.9434225 1.716392 ]\n","6,\t0.11,\t[-0.9701522 1.7852831]\n","7,\t0.06,\t[-0.98865306 1.8361537 ]\n","8,\t0.04,\t[-1.0013554 1.8737577]\n","9,\t0.02,\t[-1.0099901 1.9015862]\n","10,\t0.02,\t[-1.0157865 1.9222052]\n","11,\t0.01,\t[-1.019615 1.9375019]\n","12,\t0.01,\t[-1.0220896 1.9488654]\n","13,\t0.01,\t[-1.0236413 1.9573189]\n","14,\t0.01,\t[-1.0245715 1.963617 ]\n","15,\t0.01,\t[-1.0250894 1.9683164]\n","16,\t0.01,\t[-1.0253391 1.9718288]\n","17,\t0.01,\t[-1.0254192 1.9744583]\n","18,\t0.01,\t[-1.0253965 1.9764304]\n","19,\t0.01,\t[-1.025315 1.9779121]\n","\n","true w\t\t [-1. 2.]\n","estimated w\t [-1.025315 1.9779121]\n"]}],"source":["step_size = 0.1\n","\n","linear_module = nn.Linear(d, 1, bias=False)\n","\n","loss_func = nn.MSELoss()\n","\n","optim = torch.optim.SGD(linear_module.parameters(), lr=step_size)\n","\n","print('iter,\\tloss,\\tw')\n","\n","for i in range(20):\n"," y_hat = linear_module(X)\n"," loss = loss_func(y_hat, y)\n"," optim.zero_grad()\n"," loss.backward()\n"," optim.step()\n","\n"," print('{},\\t{:.2f},\\t{}'.format(i, loss.item(), linear_module.weight.view(2).detach().numpy()))\n","\n","print('\\ntrue w\\t\\t', true_w.view(2).numpy())\n","print('estimated w\\t', linear_module.weight.view(2).detach().numpy())"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0XiWTvd9JhxS","outputId":"7440b0e7-b246-4584-9bbe-56c2dae30568"},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light","tags":[]},"output_type":"display_data"}],"source":["visualize_fun(linear_module.weight.t(), 'Dataset with learned $w$ (PyTorch GD)')"]},{"cell_type":"markdown","metadata":{"id":"rC3kw6ftJhxT"},"source":["## Linear regression using SGD\n","In the previous examples, we computed the average gradient over the entire dataset (Gradient Descent). We can implement Stochastic Gradient Descent with a simple modification."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"fa9JMaQUJhxT","outputId":"01025aea-bfa8-44ac-ba13-6efa2ddae088","colab":{"base_uri":"https://localhost:8080/"},"executionInfo":{"status":"ok","timestamp":1698805003134,"user_tz":420,"elapsed":5,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"stream","name":"stdout","text":["iter,\tloss,\tw\n","0,\t0.01,\t[-0.16747227 0.69458336]\n","20,\t0.73,\t[-0.5277779 1.409119 ]\n","40,\t0.05,\t[-0.7416818 1.7194623]\n","60,\t0.04,\t[-0.80749375 1.8314769 ]\n","80,\t0.09,\t[-0.888827 1.8813882]\n","100,\t0.06,\t[-0.93712914 1.9570426 ]\n","120,\t0.00,\t[-0.964763 1.9772898]\n","140,\t0.00,\t[-0.9806282 1.9791763]\n","160,\t0.04,\t[-0.9831248 1.9838824]\n","180,\t0.01,\t[-0.9979536 1.9885796]\n","\n","true w\t\t [-1. 2.]\n","estimated w\t [-0.9991454 1.9860797]\n"]}],"source":["step_size = 0.01\n","\n","linear_module = nn.Linear(d, 1)\n","loss_func = nn.MSELoss()\n","optim = torch.optim.SGD(linear_module.parameters(), lr=step_size)\n","print('iter,\\tloss,\\tw')\n","for i in range(200):\n"," rand_idx = np.random.choice(n) # take a random point from the dataset\n"," x = X[rand_idx]\n"," y_hat = linear_module(x)\n"," loss = loss_func(y_hat, y[rand_idx]) # only compute the loss on the single point\n"," optim.zero_grad()\n"," loss.backward()\n"," optim.step()\n","\n"," if i % 20 == 0:\n"," print('{},\\t{:.2f},\\t{}'.format(i, loss.item(), linear_module.weight.view(2).detach().numpy()))\n","\n","print('\\ntrue w\\t\\t', true_w.view(2).numpy())\n","print('estimated w\\t', linear_module.weight.view(2).detach().numpy())"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"0tuKzHWyJhxT","outputId":"72dd607b-772c-48fe-8d57-8ea6e62f50a6","colab":{"base_uri":"https://localhost:8080/","height":432},"executionInfo":{"status":"ok","timestamp":1698805770658,"user_tz":420,"elapsed":739,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["
"],"image/png":"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\n"},"metadata":{}}],"source":["visualize_fun(linear_module.weight.t(), 'Dataset with learned $w$ (PyTorch SGD)')"]},{"cell_type":"markdown","metadata":{"id":"vhmk4YPWJhxT"},"source":["# Neural Network Basics in PyTorch\n","\n","Let's consider the dataset from hw3. We will try and fit a simple neural network to the data."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"cD2kkX3PJhxT","outputId":"9d8eda68-8781-4eef-a397-4e5b8e4f9e43","colab":{"base_uri":"https://localhost:8080/","height":474},"executionInfo":{"status":"ok","timestamp":1698805006337,"user_tz":420,"elapsed":565,"user":{"displayName":"Mingyu Lu","userId":"13021963391902492014"}}},"outputs":[{"output_type":"display_data","data":{"text/plain":["
"],"image/png":"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\n"},"metadata":{}}],"source":["%matplotlib inline\n","\n","d = 1\n","n = 200\n","X = torch.rand(n,d)\n","y = 4 * torch.sin(np.pi * X) * torch.cos(6*np.pi*X**2)\n","\n","plt.scatter(X.numpy(), y.numpy())\n","plt.title('plot of $f(x)$')\n","plt.xlabel('$x$')\n","plt.ylabel('$y$')\n","\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"JaUBFZGIJhxU"},"source":["Here we define a simple two hidden layer neural network with Tanh activations. There are a few hyper parameters to play with to get a feel for how they change the results."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"vNjfSahuJhxU","outputId":"e204d43c-dd0f-4dd8-d6a4-d1c42666f5d9"},"outputs":[{"name":"stdout","output_type":"stream","text":["iter,\tloss\n","0,\t3.96\n","600,\t3.69\n","1200,\t2.58\n","1800,\t1.10\n","2400,\t0.91\n","3000,\t0.68\n","3600,\t0.14\n","4200,\t0.08\n","4800,\t0.06\n","5400,\t0.15\n"]}],"source":["# feel free to play with these parameters\n","\n","step_size = 0.05\n","n_epochs = 6000\n","n_hidden_1 = 32\n","n_hidden_2 = 32\n","d_out = 1\n","\n","neural_network = nn.Sequential(\n"," nn.Linear(d, n_hidden_1),\n"," nn.Tanh(),\n"," nn.Linear(n_hidden_1, n_hidden_2),\n"," nn.Tanh(),\n"," nn.Linear(n_hidden_2, d_out)\n"," )\n","\n","loss_func = nn.MSELoss()\n","\n","optim = torch.optim.SGD(neural_network.parameters(), lr=step_size)\n","print('iter,\\tloss')\n","for i in range(n_epochs):\n"," y_hat = neural_network(X)\n"," loss = loss_func(y_hat, y)\n"," optim.zero_grad()\n"," loss.backward()\n"," optim.step()\n","\n"," if i % (n_epochs // 10) == 0:\n"," print('{},\\t{:.2f}'.format(i, loss.item()))\n","\n"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"ic6YX9lNJhxU","outputId":"036e3ef2-eba5-4b69-ad2b-1f4836ee4ccf"},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light","tags":[]},"output_type":"display_data"}],"source":["X_grid = torch.from_numpy(np.linspace(0,1,50)).float().view(-1, d)\n","y_hat = neural_network(X_grid)\n","plt.scatter(X.numpy(), y.numpy())\n","plt.plot(X_grid.detach().numpy(), y_hat.detach().numpy(), 'r')\n","plt.title('plot of $f(x)$ and $\\hat{f}(x)$')\n","plt.xlabel('$x$')\n","plt.ylabel('$y$')\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"mo4LEXsyJhxU"},"source":["## Useful links:\n","- [60 minute PyTorch Tutorial](https://pytorch.org/tutorials/beginner/deep_learning_60min_blitz.html)\n","- [PyTorch Docs](https://pytorch.org/docs/stable/index.html)\n","- [Lecture notes on Auto-Diff](https://courses.cs.washington.edu/courses/cse446/19wi/notes/auto-diff.pdf)\n","\n"]},{"cell_type":"markdown","metadata":{"id":"E3IIQel9JhxU"},"source":["# Appendix 1: Computation graphs\n","\n","What's special about PyTorch's `tensor` object is that it implicitly creates a computation graph in the background. A computation graph is a a way of writing a mathematical expression as a graph. There is an algorithm to compute the gradients of all the variables of a computation graph in time on the same order it is to compute the function itself.\n","\n","Consider the expression $e=(a+b)*(b+1)$ with values $a=2, b=1$. We can draw the evaluated computation graph as\n","
\n","
\n","\n","\n","\n","[source](https://colah.github.io/posts/2015-08-Backprop/)\n","\n","In PyTorch, we can write this as"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"5FgHVktiJhxU","outputId":"4cba6ba5-ddf0-4c67-dd42-4235bdb0af25"},"outputs":[{"name":"stdout","output_type":"stream","text":["c tensor(3., grad_fn=)\n","d tensor(2., grad_fn=)\n","e tensor(6., grad_fn=)\n"]}],"source":["a = torch.tensor(2.0, requires_grad=True) # we set requires_grad=True to let PyTorch know to keep the graph\n","b = torch.tensor(1.0, requires_grad=True)\n","c = a + b\n","d = b + 1\n","e = c * d\n","print('c', c)\n","print('d', d)\n","print('e', e)"]},{"cell_type":"markdown","metadata":{"id":"41qbnXe9JhxV"},"source":["We can see that PyTorch kept track of the computation graph for us."]},{"cell_type":"markdown","metadata":{"id":"nbbtIwqRJhxV"},"source":["# Appendix 2: Things that might help on the homework\n","\n","## Momentum\n","\n","There are other optimization algorithms besides stochastic gradient descent. One is a modification of SGD called momentum. We won't get into it here, but if you would like to read more [here](https://distill.pub/2017/momentum/) is a good place to start.\n","\n","We only change the step size and add the momentum keyword argument to the optimizer. Notice how it reduces the training loss in fewer iterations."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"R4xSAzouJhxV","outputId":"a1e0ce6a-2805-4877-b3eb-63ea1b936c7f"},"outputs":[{"name":"stdout","output_type":"stream","text":["iter,\tloss\n","0,\t3.83\n","150,\t3.06\n","300,\t0.74\n","450,\t0.12\n","600,\t0.04\n","750,\t0.03\n","900,\t0.01\n","1050,\t0.00\n","1200,\t0.00\n","1350,\t0.00\n"]}],"source":["# feel free to play with these parameters\n","\n","step_size = 0.05\n","momentum = 0.9\n","n_epochs = 1500\n","d = X.shape[1]\n","n_hidden_1 = 32\n","n_hidden_2 = 32\n","d_out = 1\n","\n","neural_network = nn.Sequential(\n"," nn.Linear(d, n_hidden_1),\n"," nn.Tanh(),\n"," nn.Linear(n_hidden_1, n_hidden_2),\n"," nn.Tanh(),\n"," nn.Linear(n_hidden_2, d_out)\n",")\n","\n","loss_func = nn.MSELoss()\n","\n","optim = torch.optim.SGD(neural_network.parameters(), lr=step_size, momentum=momentum)\n","print('iter,\\tloss')\n","for i in range(n_epochs):\n"," y_hat = neural_network(X)\n"," loss = loss_func(y_hat, y)\n"," optim.zero_grad()\n"," loss.backward()\n"," optim.step()\n","\n"," if i % (n_epochs // 10) == 0:\n"," print('{},\\t{:.2f}'.format(i, loss.item()))\n","\n"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"HwWOkyR-JhxV","outputId":"b8ee4197-a194-4f3c-e280-54b8f038822f"},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light","tags":[]},"output_type":"display_data"}],"source":["X_grid = torch.from_numpy(np.linspace(0,1,50)).float().view(-1, d)\n","y_hat = neural_network(X_grid)\n","plt.scatter(X.numpy(), y.numpy())\n","plt.plot(X_grid.detach().numpy(), y_hat.detach().numpy(), 'r')\n","plt.title('plot of $f(x)$ and $\\hat{f}(x)$')\n","plt.xlabel('$x$')\n","plt.ylabel('$y$')\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"D09b9CYYJhxV"},"source":["## CrossEntropyLoss\n","So far, we have been considering regression tasks and have used the [MSELoss](https://pytorch.org/docs/stable/nn.html#torch.nn.MSELoss) module. For the homework, we will be performing a classification task and will use the cross entropy loss.\n","\n","PyTorch implements a version of the cross entropy loss in one module called [CrossEntropyLoss](https://pytorch.org/docs/stable/nn.html#torch.nn.CrossEntropyLoss). Its usage is slightly different than MSE, so we will break it down here.\n","\n","- input: The first parameter to CrossEntropyLoss is the output of our network. It expects a *real valued* tensor of dimensions $(N,C)$ where $N$ is the minibatch size and $C$ is the number of classes. In our case $N=3$ and $C=2$. The values along the second dimension correspond to raw unnormalized scores for each class. The CrossEntropyLoss module does the softmax calculation for us, so we do not need to apply our own softmax to the output of our neural network.\n","- output: The second parameter to CrossEntropyLoss is the true label. It expects an *integer valued* tensor of dimension $(N)$. The integer at each element corresponds to the correct class. In our case, the \"correct\" class labels are class 0, class 1, and class 1.\n","\n","Try out the loss function on three toy predictions. The true class labels are $y=[1,1,0]$. The first two examples correspond to predictions that are \"correct\" in that they have higher raw scores for the correct class. The second example is \"more confident\" in the prediction, leading to a smaller loss. The last two examples are incorrect predictions with lower and higher confidence respectively."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"IG5_xfQpJhxW","outputId":"a4375143-99d2-4ce1-d720-c5c3b0caa28f"},"outputs":[{"name":"stdout","output_type":"stream","text":["tensor(0.1269)\n"]}],"source":["loss = nn.CrossEntropyLoss()\n","\n","input = torch.tensor([[-1., 1],[-1, 1],[1, -1]]) # raw scores correspond to the correct class\n","# input = torch.tensor([[-3., 3],[-3, 3],[3, -3]]) # raw scores correspond to the correct class with higher confidence\n","# input = torch.tensor([[1., -1],[1, -1],[-1, 1]]) # raw scores correspond to the incorrect class\n","# input = torch.tensor([[3., -3],[3, -3],[-3, 3]]) # raw scores correspond to the incorrect class with incorrectly placed confidence\n","\n","target = torch.tensor([1, 1, 0])\n","output = loss(input, target)\n","print(output)\n"]},{"cell_type":"markdown","metadata":{"id":"x3ca7xosJhxW"},"source":["## Learning rate schedulers\n","\n","Often we do not want to use a fixed learning rate throughout all training. PyTorch offers learning rate schedulers to change the learning rate over time. Common strategies include multiplying the lr by a constant every epoch (e.g. 0.9) and halving the learning rate when the training loss flattens out.\n","\n","See the [learning rate scheduler docs](https://pytorch.org/docs/stable/optim.html#how-to-adjust-learning-rate) for usage and examples"]},{"cell_type":"markdown","metadata":{"id":"JA_8CrwnJhxX"},"source":["# Appendix 3: Beyond Linear Layers\n","\n","## Convolutions\n","When working with images, we often want to use convolutions to extract features using convolutions. PyTorch implments this for us in the `torch.nn.Conv2d` module. It expects the input to have a specific dimension $(N, C_{in}, H_{in}, W_{in})$ where $N$ is batch size, $C_{in}$ is the number of channels the image has, and $H_{in}, W_{in}$ are the image height and width respectively.\n","\n","We can modify the convolution to have different properties with the parameters:\n","- kernel_size\n","- stride\n","- padding\n","\n","They can change the output dimension so be careful.\n","\n","See the [`torch.nn.Conv2d` docs](https://pytorch.org/docs/stable/nn.html#torch.nn.Conv2d) for more information."]},{"cell_type":"markdown","metadata":{"id":"MFNCKNR3JhxX"},"source":["To illustrate what the `Conv2d` module is doing, let's set the conv weights manually to a Gaussian blur kernel.\n","\n","We can see that it applies the kernel to the image."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"-ghdIfXFJhxX","outputId":"177ed056-c156-444b-cda6-d19bdbabce16"},"outputs":[{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light","tags":[]},"output_type":"display_data"},{"data":{"image/png":"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","text/plain":["
"]},"metadata":{"needs_background":"light","tags":[]},"output_type":"display_data"}],"source":["# an entire mnist digit\n","image = np.array([0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.3803922 , 0.37647063, 0.3019608 ,0.46274513, 0.2392157 , 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.3529412 , 0.5411765 , 0.9215687 ,0.9215687 , 0.9215687 , 0.9215687 , 0.9215687 , 0.9215687 ,0.9843138 , 0.9843138 , 0.9725491 , 0.9960785 , 0.9607844 ,0.9215687 , 0.74509805, 0.08235294, 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.54901963,0.9843138 , 0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 ,0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 ,0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 ,0.7411765 , 0.09019608, 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.8862746 , 0.9960785 , 0.81568635,0.7803922 , 0.7803922 , 0.7803922 , 0.7803922 , 0.54509807,0.2392157 , 0.2392157 , 0.2392157 , 0.2392157 , 0.2392157 ,0.5019608 , 0.8705883 , 0.9960785 , 0.9960785 , 0.7411765 ,0.08235294, 0., 0., 0., 0.,0., 0., 0., 0., 0.,0.14901961, 0.32156864, 0.0509804 , 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.13333334,0.8352942 , 0.9960785 , 0.9960785 , 0.45098042, 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0.32941177, 0.9960785 ,0.9960785 , 0.9176471 , 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0.32941177, 0.9960785 , 0.9960785 , 0.9176471 ,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0.4156863 , 0.6156863 ,0.9960785 , 0.9960785 , 0.95294124, 0.20000002, 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0.09803922, 0.45882356, 0.8941177 , 0.8941177 ,0.8941177 , 0.9921569 , 0.9960785 , 0.9960785 , 0.9960785 ,0.9960785 , 0.94117653, 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.26666668, 0.4666667 , 0.86274517,0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 ,0.9960785 , 0.9960785 , 0.9960785 , 0.9960785 , 0.5568628 ,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0.14509805, 0.73333335,0.9921569 , 0.9960785 , 0.9960785 , 0.9960785 , 0.8745099 ,0.8078432 , 0.8078432 , 0.29411766, 0.26666668, 0.8431373 ,0.9960785 , 0.9960785 , 0.45882356, 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0.4431373 , 0.8588236 , 0.9960785 , 0.9490197 , 0.89019614,0.45098042, 0.34901962, 0.12156864, 0., 0.,0., 0., 0.7843138 , 0.9960785 , 0.9450981 ,0.16078432, 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0.6627451 , 0.9960785 ,0.6901961 , 0.24313727, 0., 0., 0.,0., 0., 0., 0., 0.18823531,0.9058824 , 0.9960785 , 0.9176471 , 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0.07058824, 0.48627454, 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.32941177, 0.9960785 , 0.9960785 ,0.6509804 , 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0.54509807, 0.9960785 , 0.9333334 , 0.22352943, 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.8235295 , 0.9803922 , 0.9960785 ,0.65882355, 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0.9490197 , 0.9960785 , 0.93725497, 0.22352943, 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.34901962, 0.9843138 , 0.9450981 ,0.3372549 , 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.01960784,0.8078432 , 0.96470594, 0.6156863 , 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0.01568628, 0.45882356, 0.27058825,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0., 0.,0., 0., 0., 0.], dtype=np.float32)\n","image_torch = torch.from_numpy(image).view(1, 1, 28, 28)\n","\n","# a gaussian blur kernel\n","gaussian_kernel = torch.tensor([[1., 2, 1],[2, 4, 2],[1, 2, 1]]) / 16.0\n","\n","conv = nn.Conv2d(1, 1, 3)\n","# manually set the conv weight\n","conv.weight.data[:] = gaussian_kernel\n","\n","convolved = conv(image_torch)\n","\n","plt.title('original image')\n","plt.imshow(image_torch.view(28,28).detach().numpy())\n","plt.show()\n","\n","plt.title('blurred image')\n","plt.imshow(convolved.view(26,26).detach().numpy())\n","plt.show()"]},{"cell_type":"markdown","metadata":{"id":"1muk73M1JhxX"},"source":["As we can see, the image is blurred as expected.\n","\n","In practice, we learn many kernels at a time. In this example, we take in an RGB image (3 channels) and output a 16 channel image. After an activation function, that could be used as input to another `Conv2d` module."]},{"cell_type":"code","execution_count":null,"metadata":{"id":"RaSnBMsYJhxX","outputId":"08a61fd3-5e0a-4af7-bf81-8863842c9a55"},"outputs":[{"name":"stdout","output_type":"stream","text":["im shape torch.Size([4, 3, 32, 32])\n","convolved im shape torch.Size([4, 16, 30, 30])\n"]}],"source":["im_channels = 3 # if we are working with RGB images, there are 3 input channels, with black and white, 1\n","out_channels = 16 # this is a hyperparameter we can tune\n","kernel_size = 3 # this is another hyperparameter we can tune\n","batch_size = 4\n","image_width = 32\n","image_height = 32\n","\n","im = torch.randn(batch_size, im_channels, image_width, image_height)\n","\n","m = nn.Conv2d(im_channels, out_channels, kernel_size)\n","convolved = m(im) # it is a module so we can call it\n","\n","print('im shape', im.shape)\n","print('convolved im shape', convolved.shape)"]},{"cell_type":"markdown","metadata":{"id":"tcjWN--eJhxX"},"source":["## Recurrent Cells (or Recurrent Neural Networks)"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"80Bw2G-RJhxY"},"outputs":[],"source":["def process_corpus(corpus, sentence_length):\n"," \"\"\"\n"," Arguments:\n"," corpus (str) -- Continous text. Can be anything but should be relatively long.\n"," sentence_length (int) -- Size of each sentence in the output.\n"," Does not have to be divisible by # of words in corpus, in which case end will be padded.\n"," Returns:\n"," Tuple of size 4 containing:\n"," - Train Input - shape (batch, sentence) containing indexes of words for each sentence.\n"," - Train Truth - Same as Train Input but contains index of the next word in a given sentence.\n"," - Word to Index Dictionary - Dictionary for each word containing a corresponding integer.\n"," - Index to Word Dictionary - Reverse of Word to Index Dictionary.\n","\n"," Example:\n"," process_corpus(\"Sam likes cats\", 2) outputs:\n"," - [[1, 2], [3, 0]]\n"," - [[2, 3], [0, 0]]\n"," - {\"\": 0, \"Sam\": 1, \"likes\": 2, \"cats\": 3}\n"," - {0: \"\", 1: \"Sam\", 2: \"likes\", 3: \"cats\"}\n"," \"\"\"\n"," # Let's make corpus a list of words\n"," corpus = corpus.split()\n"," # QUESTION: Should we also trim/lowercase the words here? Is \"You,\" vs. \"you\" very different?\n","\n"," # Then split it into smaller sentences of size sentence_length\n"," x = []\n"," y = []\n"," for idx in range(0, len(corpus), sentence_length):\n"," x.append(corpus[idx: idx + sentence_length])\n"," # Since we are trying to predict the next word y's are just x's shifted by one\n"," y.append(corpus[idx + 1: idx + sentence_length + 1])\n"," # Last sentences might be shorter. Let's pad it with something smaller\n"," x[-1] += [\"\" for _ in range(sentence_length - len(x[-1]))]\n"," y[-1] += [\"\" for _ in range(sentence_length - len(y[-1]))]\n","\n"," # Create dictionary from words to indices and vice-versa\n"," # QUESTION: Is \"\" a good choice for end-of-sentence tag? Maybe we should pad beginning of the sentences too?\n"," idx_to_word = {0: \"\"}\n"," word_to_idx = {\"\": 0}\n"," idx = 1\n"," for sentence in x:\n"," for word in sentence:\n"," if word not in word_to_idx:\n"," word_to_idx[word] = idx\n"," idx_to_word[idx] = word\n"," idx += 1\n","\n"," x_idx = torch.tensor([[word_to_idx[w] for w in s] for s in x]).long()\n"," y_idx = torch.tensor([[word_to_idx[w] for w in s] for s in y]).long()\n","\n"," return x_idx, y_idx, word_to_idx, idx_to_word"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"tLWThiQ3JhxY","outputId":"4dcfdf65-70c2-4f76-9595-b5b1375bb950"},"outputs":[{"name":"stdout","output_type":"stream","text":["Sequential(\n"," (0): Embedding(61, 10)\n"," (1): RNN(10, 5, batch_first=True)\n",")\n","0,\t4.21\n","100,\t3.76\n","200,\t3.32\n","300,\t2.91\n","400,\t2.57\n","500,\t2.29\n","600,\t2.06\n","700,\t1.89\n","800,\t1.75\n","900,\t1.62\n"]}],"source":["# Feel free to play with parameters\n","embedding_size = 10\n","sentence_length = 5\n","hidden_size = 5\n","n_epochs = 1000\n","\n","# Dataset\n","corpus = \"Hey, you. You’re finally awake. \" \\\n"," \"You were trying to cross the border, right? \" \\\n"," \"Walked right into that Imperial ambush, \" \\\n"," \"same as us, and that thief over there. \" \\\n"," \"Skyrim was fine until you came along. \" \\\n"," \"Empire was nice and lazy. \" \\\n"," \"If they hadn’t been looking for you, \" \\\n"," \"I could’ve stolen that horse and been half way to Hammerfell. \" \\\n"," \"You there. You and me — we should be here. \" \\\n"," \"It’s these Stormcloaks the Empire wants. \"\n","\n","x, y, word_to_idx, idx_to_word = process_corpus(corpus, sentence_length)\n","\n","model_rnn = nn.Sequential(\n"," nn.Embedding(len(idx_to_word), embedding_size),\n"," nn.RNN(embedding_size, hidden_size, batch_first=True),\n",")\n","# Linear model has to be separate, because we'll be using only first output of the RNN\n","linear = nn.Linear(hidden_size, len(idx_to_word))\n","print(model_rnn)\n","\n","criterion = nn.CrossEntropyLoss()\n","optimizer = torch.optim.Adam(list(model_rnn.parameters()) + list(linear.parameters()))\n","\n","for i in range(n_epochs):\n"," x_mid, _ = model_rnn(x)\n"," y_hat = linear(x_mid).transpose(1, 2) # This makes shape correct for the Loss\n"," loss = criterion(y_hat, y)\n"," optimizer.zero_grad()\n"," loss.backward()\n"," optimizer.step()\n","\n"," if i % (n_epochs // 10) == 0:\n"," print('{},\\t{:.2f}'.format(i, loss.item()))"]},{"cell_type":"code","execution_count":null,"metadata":{"id":"BNZmvY9cJhxY","outputId":"a1c651d2-ec14-42c0-a0ee-94dc4c32d451"},"outputs":[{"name":"stdout","output_type":"stream","text":["Truth: ['you.', 'You’re', 'finally', 'awake.', 'You']\n","Predict: ['you.', 'You’re', 'finally', 'right', 'You']\n","horse and been half way and been half way and been half way and been half\n"]}],"source":["# Let's see a prediction for the first sentence\n","with torch.no_grad():\n"," y_hat = linear(model_rnn(x)[0])\n"," y_hat = torch.argmax(y_hat, dim=2)\n"," sentences_hat = [[idx_to_word[int(w)] for w in s] for s in y_hat]\n"," sentences_true = [[idx_to_word[int(w)] for w in s] for s in y]\n","\n"," sentence_idx = 0\n"," print(f\"Truth: {sentences_true[sentence_idx]}\")\n"," print(f\"Predict: {sentences_hat[sentence_idx]}\")\n","\n","# Lets have a custom sentence, with a random word starting.\n","with torch.no_grad():\n"," word = \"horse\"\n"," sentence = f\"{word}\"\n"," for _ in range(15):\n"," word_idx = torch.tensor([word_to_idx[word]]).reshape(1, 1)\n"," y_hat, _ = model_rnn(word_idx)\n"," y_hat = linear(y_hat)\n"," y_hat = torch.argmax(y_hat, dim=2)\n"," word = idx_to_word[y_hat.reshape(1).item()]\n"," sentence += f\" {word}\"\n"," print(sentence)\n"," # See how it repeats itself near the end? There are ways of fixing it!"]},{"cell_type":"markdown","metadata":{"id":"jUBTfUq3JhxY"},"source":["## Useful links:\n","- [60 minute PyTorch Tutorial](https://pytorch.org/tutorials/beginner/deep_learning_60min_blitz.html)\n","- [PyTorch Docs](https://pytorch.org/docs/stable/index.html)\n","- [Lecture notes on Auto-Diff](https://courses.cs.washington.edu/courses/cse446/19wi/notes/auto-diff.pdf)\n","\n"]}],"metadata":{"colab":{"provenance":[]},"kernelspec":{"display_name":"Python 3","language":"python","name":"python3"},"language_info":{"codemirror_mode":{"name":"ipython","version":3},"file_extension":".py","mimetype":"text/x-python","name":"python","nbconvert_exporter":"python","pygments_lexer":"ipython3","version":"3.7.10"}},"nbformat":4,"nbformat_minor":0}